// Arguments: Ints, Ints, Doubles, Doubles
#include <stan/math/prim.hpp>
#include <boost/math/special_functions/binomial.hpp>

using stan::math::var;
using std::numeric_limits;
using std::vector;

class AgradCdfLogBetaBinomial : public AgradCdfLogTest {
 public:
  void valid_values(vector<vector<double> >& parameters,
                    vector<double>& cdf_log) {
    vector<double> param(4);

    param[0] = 17;  // n
    param[1] = 45;  // N
    param[2] = 13;  // alpha
    param[3] = 15;  // beta
    parameters.push_back(param);
    cdf_log.push_back(std::log(
        0.2680523296111902594541368047465042591108987357277389728827508022844102288442195709664943608618480998));  // expected cdf_log
  }

  void invalid_values(vector<size_t>& index, vector<double>& value) {
    // N
    index.push_back(1U);
    value.push_back(-1);

    // alpha
    index.push_back(2U);
    value.push_back(-1);

    // beta
    index.push_back(3U);
    value.push_back(-1);
  }

  bool has_lower_bound() { return false; }

  bool has_upper_bound() { return false; }

  template <typename T_n, typename T_N, typename T_size1, typename T_size2,
            typename T4, typename T5>
  stan::return_type_t<T_size1, T_size2> cdf_log(const T_n& n, const T_N& N,
                                                const T_size1& alpha,
                                                const T_size2& beta, const T4&,
                                                const T5&) {
    return stan::math::beta_binomial_cdf_log(n, N, alpha, beta);
  }

  template <typename T_n, typename T_N, typename T_size1, typename T_size2,
            typename T4, typename T5>
  stan::return_type_t<T_size1, T_size2> cdf_log_function(const T_n& n,
                                                         const T_N& N,
                                                         const T_size1& alpha,
                                                         const T_size2& beta,
                                                         const T4&, const T5&) {
    using boost::math::binomial_coefficient;
    using stan::math::lbeta;
    using std::exp;

    stan::return_type_t<T_size1, T_size2> cdf(0);

    for (int i = 0; i <= n; i++) {
      cdf += binomial_coefficient<double>(N, i)
             * exp(lbeta(alpha + i, N - i + beta) - lbeta(alpha, beta));
    }

    return log(cdf);
  }
};
